How to combat atmospheric carbon dioxide along with development activities? A mathematical model

Abstract

Depletion in forest density due to development activities is one of the reasons for the elevated level of carbon dioxide (CO2). In this scenario, the plantation of leafy trees, which absorb more CO2 compared to regular trees, under a planned strategy may help to attain the desired level of atmospheric carbon dioxide. We have formulated a non-linear mathematical model concerning the strategy of maintaining the atmospheric level of CO2 along with development activities and analyzed the proportion of deforested land needed for the plantation of leafy trees. This strategy will ensure that the absorption of carbon dioxide remains at its previous level. To study the long-term behavior of the formulated model system, we employ the qualitative theory of differential equations. We have derived sufficient conditions under which all the considered dynamical variables settle to their equilibrium level. After analyzing the formulated model system, we find that the system undergoes Hopf and transcritical bifurcations with respect to the deforestation rate. Furthermore, numerical simulations have been carried out to support the analytically obtained results. Through simulation, we have determined the proportion of cleared land that should be utilized for the plantation of leafy trees to maintain the level of atmospheric CO2.